A276953 Square array A(row,col) read by antidiagonals: A(1,col) = A273670(col-1), and for row > 1, A(row,col) = A153880(A(row-1,col)); Dispersion of factorial base shift A153880 (array transposed).

1, 3, 2, 4, 8, 6, 5, 12, 30, 24, 7, 14, 48, 144, 120, 9, 26, 54, 240, 840, 720, 10, 32, 126, 264, 1440, 5760, 5040, 11, 36, 150, 744, 1560, 10080, 45360, 40320, 13, 38, 168, 864, 5160, 10800, 80640, 403200, 362880, 15, 50, 174, 960, 5880, 41040, 85680, 725760, 3991680, 3628800, 16, 56, 246, 984, 6480, 46080, 367920, 766080, 7257600, 43545600, 39916800

Offset: 1

Author

Antti Karttunen, Sep 22 2016

Keywords

• nonn
• base
• tabl

Comments

The array A(row,col) is read by descending antidiagonals: A(1,1), A(1,2), A(2,1), A(1,3), A(2,2), A(3,1), etc.

Entries on row n are all multiples of n!. Dividing that factor out gives another array A276616.

Examples

			The top left corner of the array:
    1,    3,     4,     5,     7,     9,    10,    11,    13,    15,    16
    2,    8,    12,    14,    26,    32,    36,    38,    50,    56,    60
    6,   30,    48,    54,   126,   150,   168,   174,   246,   270,   288
   24,  144,   240,   264,   744,   864,   960,   984,  1464,  1584,  1680
  120,  840,  1440,  1560,  5160,  5880,  6480,  6600, 10200, 10920, 11520
  720, 5760, 10080, 10800, 41040, 46080, 50400, 51120, 81360, 86400, 90720
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..1830; the first 60 antidiagonals of array
• Index entries for sequences related to factorial base representation
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Inverse permutation: A276954.

Transpose: A276955.

Cf. A276949 (index of row where n appears), A276951 (index of column).

Cf. A153880, A273670.

Row 1: A273670, Row 2: A276932, Row 3: A276933.

Column 1: A000142. For other columns, see the rows of transposed array A276955.

Related or similar permutations: A257503, A275848, A273666.

Cf. also arrays A276616, A276589 & A276943.

Programs

Scheme

(define (A276953 n) (A276953bi (A002260 n) (A004736 n)))
(define (A276953bi row col) (if (= 1 row) (A273670 (- col 1)) (A153880 (A276953bi (- row 1) col))))

Formula

A(1,col) = A273670(col-1), and for row > 1, A(row,col) = A153880(A(row-1,col))

As a composition of other permutations:

a(n) = A275848(A257503(n)).

Other identities. For all n >= 1:

A(A276949(n),A276951(n)) = n.